Driving through Toronto earlier this week I saw a shiny black 4x4 with an English flag sticking out of one side window and a German flag out of the other. Presumably a Canadian family of mixed English and German origin, so rooting for both teams in the World Cup. A little later I saw a car with the Portuguese flag on one side and the Italian on the other. It occurred to me that this pretty much sums up what we've been trying to achieve in Europe since the second world war. Welcome to the European Union - in Canada.

In fact, why doesn't the European Union invite Canada to join at once? In most respects it would be a much easier fit than Ukraine, let alone Turkey. It effortlessly meets the EU's so-called Copenhagen criteria for membership, including democratic government, the rule of law, a well-regulated market economy and respect for minority rights (Canada's a world-leader on that). Canada is rich, so would be a much-needed net contributor to the European budget at a time when the EU has been taking in lots of poorer states. One of Europe's besetting weaknesses is disagreement between the British and the French, but on this the two historic rivals would instantly agree. English-speaking Canada would strengthen the Anglophone group in the EU, Quebec the Francophone.

Take the list of things that many Europeans consider to be most characteristic of us - by contrast with the United States. We Europeans believe that the free market should be tamed by values of social justice, solidarity and inclusiveness, realised through a strong welfare state. We don't have capital punishment. We believe that military force should only be used as a last resort and with the sanction of international law. We support international organisations. We love multilateralism and abhor unilateralism. We tend to think that men and women should be able to live more or less as they please with whomever they please, irrespective of gender and sexual orientation. We pride ourselves on our diversity. Check, check, check. Welcome to Canada.

Look a little closer at the opinion surveys, and there are a few distinguishing marks. Canadians still tend to place a little more store by self-reliance and the woodsman frontier spirit than most Europeans. Canadians tend to be a bit more religious than most Europeans - though not more than the Poles or Ukrainians. Most important, their attitude to immigration and ethnic minorities is more positive than that of most Europeans. But these differences in attitudes could easily be accommodated within the wide spectrum of today's EU, while a Canadian-style embrace of immigration and ethnic minorities would do Europe a power of good.

OK, I know it's not going to happen. After saying yes to Turkey, the EU is having difficulty finding clear and consistent grounds for saying no to other, still more remote candidates - but being in the general vicinity of Europe does seem to be a continuing requirement. Now I guess an agile Canadian Inuk could traverse the melting ice floes to Greenland, which actually belonged to the EU for 12 years and now has a special treaty relationship with it. From there it's a relatively short boat trip to Iceland, which is generally considered to be a European country.

But it would be hard to argue with a straight face that Canada is in Europe. Moreover, with some 85% of its exports going to the United States, and so many of its business, energy and human links running north-south across the border, Canada is increasingly integrated into the US economy. The price the EU demands for opening its internal borders to new members is that they should tighten up their external border with non-EU neighbours. That would be a tall order for Canada, along the longest frontier on earth, with the most powerful neighbour on earth.

This mildly amusing thought experiment - Canada as EU member - has a serious point. To look at Canada and its values is to understand how foolish it is to try to define Europe by reference to an allegedly unique set of "European values". Values matter, but these European values are shared by most Canadians more than they are by many Europeans. And many of these values are also shared by Americans in the liberal blue states of the US.

Yet another thing Canadians and Europeans have in common is an obsession with the United States, and with distinguishing themselves from it, often by crude stereotyping. A Canadian writer observes that his compatriots "love to yell about how modest we are". Just like today's Europeans. Canadians and Europeans enjoy wallowing in a sense of moral superiority towards the imperial hyperpower, while doing rather little to improve the world outside their borders. Canada's defence spending, at around 1.2% of GDP, is low even by European standards. (Among Nato members, only Luxembourg and Iceland spend less.) So is its foreign-aid budget, a mere 0.27% of GDP in 2004 - despite the fact that it was the Canadian statesman Lester Pearson who more than 30 years ago proposed what has become the UN target of developed countries spending 0.7% of GDP on foreign aid. There is the arrogance of power, but there is also the arrogance of impotence.

Yet this impotence is self-imposed. The potential power - military, economic and soft - of the established liberal democracies outside the US is enormous. The three largest sets are the democracies of Europe, most but not all gathered in the EU; the Anglosphere/Commonwealth democracies, including Australia, New Zealand, Canada (intersecting with the Francosphere), South Africa and India (the world's largest democracy); and the Hispanosphere and Lusosphere democracies of Latin America. Between us, we have a combined GDP much larger than that of the US, as well as natural resources and specific strengths that the hyperpower cannot match. Instead of sitting round like a bunch of poor cousins, complaining all the time about the behaviour of the rich American uncle, we should be thinking what we ourselves can do to make a difference beyond our shores.

Canada, for example, has a tradition of peacekeeping that it is now (controversially) extending to more combative peacemaking in Afghanistan. With its profusion of natural riches, and its outsize share of the world's ice and snow, it has a unique contribution to make in crafting international environmental policies and the battle against the effects of climate change.

With its carefully balanced federal model, securing the rights of a multicultural society in a bilingual framework, it has unique constitutional experience to offer the many multi-ethnic countries around the world that are struggling to avoid a fledgling democracy becoming a tyranny of the majority - and hence a catalyst for renewed ethnic conflict. Why not share this experience, in a distinctive Canadian version of democracy promotion? Or do we think the promotion of democracy should be left entirely to the Bush administration, while we sit on the sidelines and jeer?

So, in this respect at least, I return from Toronto wishing Canadians would be just a little less European. But then, in this respect, I also wish Europeans would be a little less Canadian.